Required math: algebra, functions, limits Required physics: elementary kinematics Physics frequently requires the calculation of the rate of change of one variable with respect to another. (For a discussion of one such case – the notion of velocity – see here .) If, for example, we want to calculate the velocity of a mass, we can begin by measuring its position at two distinct times and then dividing the distance travelled by the time taken to travel that distance. This will give us the average velocity over that time interval, but it won’t tell us what precise velocity the mass had at any specific time within that interval. We can get a better and better approximation to the velocity at a particular time by taking measurements at time intervals that are closer and closer together, but we are still calculating just the average velocity over a time interval, no matter how short that interval may be. If we tried to use this measurement technique for finding the velocity at once exact instant in time, we would need to take two measurements of the mass’s position at the same time.

These two measurements would, of course, be identical so if we attempted to calculate the velocity at that time by dividing the distance travelled by the time interval, we would have to divide zero by zero, which is mathematically forbidden. As we showed here , the mathematical idea of the limit of a function can be used for finding the value of that function at places where such as things as division by zero occur. So what we would like to do is to define a function that gives the average speed of the mass by the usual method of dividing the distance travelled by the time interval, and then take the limit of that function as the time interval approaches zero. Hopefully, this limit will yield a finite value that we can interpret as the velocity at a specific time. This notion of the rate of change of one quantity with respect to another is the motivation for the derivative of a function with respect to the variable . The derivative gives us the rate of change of a function at each individual point. Going back to the discussion about our speed as we walk along a north-south path, suppose we represent our position on the path as a function of time: .

The method we used earlier to calculate our average velocity was to measure how far we moved and then divide by the time taken to move that far. If we are at a position at time (that’s our starting point) and then we move to position at time is Clearly we can’t use this formula directly if both times are the same ( ) since that would involve dividing zero by zero. However, as we saw in the page where we discussed limits, that is exactly the kind of problem we solved there. We can change the notation slightly so we have a better grasp of what we’re trying to do. If we take as the reference time, then we can write the later time as and the speed formula becomes Now if we can calculate the limit as the time interval goes to zero, we should get what we’re looking for: a formula that gives us the speed at one specific point, rather than an average speed over a finite time interval. In order to proceed further, we would have to know the function , but we have the general idea of a derivative here. The derivative of a function is the rate of change with respect to t of the function at each point (provided the original function is defined at that point).

The usual notation for the derivative is: When you study differential calculus, you will encounter formulas for finding the derivatives of all the standard functions such as polynomials, exponentials, trigonometric functions, logarithms and so forth. However, all of these derivatives satisfy the definition we have just given. As an example, the page on which kinetic energy is discussed shows that if a constant force acts on a mass located at the origin for a time , then the mass’s position at that time is where is the acceleration produced by the mass (which is just from Newton’s law). We also showed on that page that the mass’s velocity at time is Now, since we know that velocity is rate of change of position, then if we calculate the derivative of with respect to time , we should get the equation for the velocity. Those who have studied calculus before will see that this is true already, but let’s apply the definition of the derivative above and see if we can prove it. We want to calculate as we hoped. Note that we are able to take the factor of outside the limit, since is a constant here.

The key to calculating formulas for derivatives is to transform the expression of which you want the limit to a form where you’re not dividing by zero, and we managed to achieve this above in the second-to-last line, where we were able to cancel the factor of off the numerator and denominator. There are formulas which can be derived in similar ways for all the standard algebraic, logarithmic, exponential and trigonometric functions, as well as standard formulas for products and quotients of functions and for compound functions (functions of other functions). However, what is important to us here is that the derivative is the answer to the physics problem of how to calculate rates of change at specific points. Acceleration 1-D Kinematics - Lesson 1 - Describing Motion with Words Acceleration Speed and Velocity Acceleration The final mathematical quantity discussed in Lesson 1 is acceleration. An often confused quantity, acceleration has a meaning much different than the meaning associated with it by sports announcers and other individuals. The definition of acceleration is: Acceleration is a vector quantity that is defined as the rate at which an object changes its velocity . An object is accelerating if it is changing its velocity. Sports announcers will occasionally say that a person is accelerating if he/she is moving fast.

Yet acceleration has nothing to do with going fast. A person can be moving very fast and still not be accelerating. Acceleration has to do with changing how fast an object is moving. If an object is not changing its velocity, then the object is not accelerating. The data at the right are representative of a northward-moving accelerating object. The velocity is changing over the course of time. In fact, the velocity is changing by a constant amount - 10 m/s - in each second of time. Anytime an object's velocity is changing, the object is said to be accelerating; it has an acceleration. The Meaning of Constant Acceleration Sometimes an accelerating object will change its velocity by the same amount each second. As mentioned in the previous paragraph, the data table above show an object changing its velocity by 10 m/s in each consecutive second. This is referred to as a constant acceleration since the velocity is changing by a constant amount each second. An object with a constant acceleration should not be confused with an object with a constant velocity. Don't be fooled! If an object is changing its velocity -whether by a constant amount or a varying amount - then it is an accelerating object. And an object with a constant velocity is not accelerating.

The data tables below depict motions of objects with a constant acceleration and a changing acceleration. Note that each object has a changing velocity. Since accelerating objects are constantly changing their velocity, one can say that the distance traveled/time is not a constant value. A falling object for instance usually accelerates as it falls. If we were to observe the motion of a free-falling object ( free fall motion will be discussed in detail later), we would observe that the object averages a velocity of approximately 5 m/s in the first second, approximately 15 m/s in the second second, approximately 25 m/s in the third second, approximately 35 m/s in the fourth second, etc. Our free-falling object would be constantly accelerating. Given these average velocity values during each consecutive 1-second time interval, we could say that the object would fall 5 meters in the first second, 15 meters in the second second (for a total distance of 20 meters), 25 meters in the third second (for a total distance of 45 meters), 35 meters in the fourth second (for a total distance of 80 meters after four seconds). These numbers are summarized in the table below.

0 s to End of Interval 0 – 1.0 s Note: The ~ symbol as used here means approximately. This discussion illustrates that a free-falling object that is accelerating at a constant rate will cover different distances in each consecutive second. Further analysis of the first and last columns of the data above reveal that there is a square relationship between the total distance traveled and the time of travel for an object starting from rest and moving with a constant acceleration. The total distance traveled is directly proportional to the square of the time. As such, if an object travels for twice the time, it will cover four times (2^2) the distance; the total distance traveled after two seconds is four times the total distance traveled after one second. If an object travels for three times the time, then it will cover nine times (3^2) the distance; the distance traveled after three seconds is nine times the distance traveled after one second. Finally, if an object travels for four times the time, then it will cover 16 times (4^2) the distance; the distance traveled after four seconds is 16 times the distance traveled after one second.

For objects with a constant acceleration, the distance of travel is directly proportional to the square of the time of travel. Calculating the Average Acceleration The average acceleration (a) of any object over a given interval of time (t) can be calculated using the equation This equation can be used to calculate the acceleration of the object whose motion is depicted by the velocity-time data table above. The velocity-time data in the table shows that the object has an acceleration of 10 m/s/s. The calculation is shown below. Acceleration values are expressed in units of velocity/time. Typical acceleration units include the following: m/s/s km/hr/s m/s2 These units may seem a little awkward to a beginning physics student. Yet they are very reasonable units when you begin to consider the definition and equation for acceleration. The reason for the units becomes obvious upon examination of the acceleration equation. Since acceleration is a velocity change over a time, the units on acceleration are velocity units divided by time units - thus (m/s)/s or (mi/hr)/s. The (m/s)/s unit can be mathematically simplified to m/s2. The Direction of the Acceleration Vector Since acceleration is a vector quantity , it has a direction associated with it.

The direction of the acceleration vector depends on two things: whether the object is speeding up or slowing down whether the object is moving in the + or - direction The general principle for determining the acceleation is: If an object is slowing down, then its acceleration is in the opposite direction of its motion. This general principle can be applied to determine whether the sign of the acceleration of an object is positive or negative, right or left, up or down, etc. Consider the two data tables below. In each case, the acceleration of the object is in the positive direction. In Example A, the object is moving in the positive direction (i.e., has a positive velocity) and is speeding up. When an object is speeding up, the acceleration is in the same direction as the velocity. Thus, this object has a positive acceleration. In Example B, the object is moving in the negative direction (i.e., has a negative velocity) and is slowing down. According to our general principle, when an object is slowing down, the acceleration is in the opposite direction as the velocity. Thus, this object also has a positive acceleration. This same general principle can be applied to the motion of the objects represented in the two data tables below.

In each case, the acceleration of the object is in the negative direction. In Example C, the object is moving in the positive direction (i.e., has a positive velocity) and is slowing down. According to our principle, when an object is slowing down, the acceleration is in the opposite direction as the velocity. Thus, this object has a negative acceleration. In Example D, the object is moving in the negative direction (i.e., has a negative velocity) and is speeding up. When an object is speeding up, the acceleration is in the same direction as the velocity. Thus, this object also has a negative acceleration. Observe the use of positive and negative as used in the discussion above (Examples A - D). In physics, the use of positive and negative always has a physical meaning. It is more than a mere mathematical symbol. As used here to describe the velocity and the acceleration of a moving object, positive and negative describe a direction. Both velocity and acceleration are vector quantities and a full description of the quantity demands the use of a directional adjective. North, south, east, west, right, left, up and down are all directional adjectives. Physics often borrows from mathematics and uses the + and - symbols as directional adjectives.

Consistent with the mathematical convention used on number lines and graphs, positive often means to the right or up and negative often means to the left or down. So to say that an object has a negative acceleration as in Examples C and D is to simply say that its acceleration is to the left or down (or in whatever direction has been defined as negative). Negative accelerations do not refer acceleration values that are less than 0. An acceleration of -2 m/s/s is an acceleration with a magnitude of 2 m/s/s that is directed in the negative direction. We Would Like to Suggest ... Sometimes it isn't enough to just read about it. You have to interact with it! And that's exactly what you do when you use one of The Physics Classroom's Interactives. We would like to suggest that you combine the reading of this page with the use of our Name That Motion Interactive. It is found in the Physics Interactive section and allows a learner to apply concepts of speed, velocity and acceleration. Position, Displacement, Velocity, and Acceleration as Vectors About Watch and Favorite Watch Watching this resources will notify you when proposed changes or new versions are created so you can keep track of improvements that have been made.

Favorite Favoriting this resource allows you to save it in the “My Resources” tab of your account. There, you can easily access this resource later when you’re ready to customize it or assign it to your students. Position, Displacement, Velocity, and Acceleration as Vectors Position, displacement, velocity, and acceleration can all be shown vectors since they are defined in terms of a magnitude and a direction. Learning Objective Examine the applications of vectors in analyzing physical quantities Key Points Vectors are arrows consisting of a magnitude and a direction. They are used in physics to represent physical quantities that also have both magnitude and direction. Displacement is a physics term meaning the distance of an object from a reference point. Since the displacement contains two pieces of information: the distance from the reference point and the direction away from the point, it is well represented by a vector. Velocity is defined as the rate of change in time of the displacement. To know the velocity of an object one must know both how fast the displacement is changing and in what direction. Therefore it is also well represented by a vector. Acceleration , being the rate of change of velocity also requires both a magnitude and a direction relative to some coordinates .

When drawing vectors, you often do not have enough space to draw them to the scale they are representing, so it is important to denote somewhere what scale they are being drawn at. Terms The rate of change of displacement with respect to change in time. Example Figure 1 shows an example of how to use a vector to visually represent an object in physics. Full Text Use of Vectors Vectors can be used to represent physical quantities. Most commonly in physics, vectors are used to represent displacement, velocity, and acceleration. Vectors are a combination of magnitude and direction, and are drawn as arrows. The length represents the magnitude and the direction of that quantity is the direction in which the vector is pointing. Because vectors are constructed this way, it is helpful to analyze physical quantities (with both size and direction) as vectors. Applications In physics, vectors are useful because they can visually represent position , displacement, velocity and acceleration. When drawing vectors, you often do not have enough space to draw them to the scale they are representing, so it is important to denote somewhere what scale they are being drawn at.

For example, when drawing a vector that represents a magnitude of 100, one may draw a line that is 5 units long at a scale of $\displaystyle \frac{1}{20}$ . When the inverse of the scale is multiplied by the drawn magnitude, it should equal the actual magnitude. Position and Displacement Displacement is defined as the distance, in any direction, of an object relative to the position of another object. Physicists use the concept of a position vector as a graphical tool to visualize displacements. A position vector expresses the position of an object from the origin of a coordinate system. A position vector can also be used to show the position of an object in relation to a reference point, secondary object or initial position (if analyzing how far the object has moved from its original location). The position vector is a straight line drawn from the arbitrary origin to the object. Once drawn, the vector has a length and a direction relative to the coordinate system used. Velocity Velocity is also defined in terms of a magnitude and direction. To say that something is gaining or losing velocity one must also say how much and in what direction.

For example, an airplane flying at 200 $\frac{km}{h}$ to the northeast can be represented by an vector pointing in the northeast direction with a magnitude of 200 $\frac{km}{h}$ . In drawing the vector, the magnitude is only important as a way to compare two vectors of the same units. So, if there were another airplane flying 100 $\frac{km}{h}$ to the southwest, the vector arrow should be half as long and pointing in the direction of southwest. Acceleration Acceleration, being the time rate of change of velocity, is composed of a magnitude and a direction, and is drawn with the same concept as a velocity vector. A value for acceleration would not be helpful in physics if the magnitude and direction of this acceleration was unknown, which is why these vectors are important. In a free body diagram , for example, of an object falling, it would be helpful to use an acceleration vector near the object to denote its acceleration towards the ground. If gravity is the only force acting on the object, this vector would be pointing downward with a magnitude of 9.81 $\frac{m}{s^2}$ What is the rate of change in velocity?

| Reference.com What is the rate of change in velocity? A: Quick Answer The rate of change in velocity is called acceleration. In the study of mechanics, acceleration is computed as it relates to time with a final unit of distance over time squared. Full Answer To compute the rate of change in velocity, or acceleration, of an object, the initial speed is subtracted from the final speed. This rate is then divided by the total length of the time period for the acceleration. For example, if a car traveled on a road for two hours and was going 30 mph at the beginning of the road and 60 mph at the end of the road, the rate of change is calculated by subtracting 30 from 60 to get a 30 mph difference. Then, the 30 miles per hour is divided by the total time of 2 hours for an acceleration result of 15 miles per hour squared. In physics, what is the definition of time? - Quora Quora Physics In physics, what is the definition of time? How would you respond to the argument that time is not real and is merely a cognitive construct that facilitates our mental perception of motion or physical change?

Written Aug 8, 2014 For some reason scientists are trapped by the unquestioned assumption that "What is Time?" is a science problem, and will hence have a "science" answer. In Time Reborn ((2013, all) Professor Lee Smolin struggles to make sense of the destination science has achieved with time - it doesn’t add up - science has failed. Space-time seems to be a sticking point, particularly for scientists. Einstein showed that space and time are connected. And he did this, did he not, without a full understanding of what time is (or did he just not share that wisdom?) So breaking down time does impact on what we think we understand space-time to be. But the starting point to that has to be to understand time itself. Why is the question of "what is time" supposedly a science problem? Time makes no causal impact, it has no outcomes, it doesn’t do anything; there’s nothing to evidence it has an existence - you can't see it, hear it, smell it or touch it (all we observe are events). It's not like speculating about say, gravity - where the effects of gravity can be seen, proved and hypothesized.

Time causes nothing, affects nothing and produces nothing. How can it be a science problem then? ["Doesn't time cause ageing?" I hear you cry. Well, no. You age because of the complex bio-chemistry events happening in your body - time is merely a measure of the results of that process.Time measures, it doesn't cause.] With no evidence to suggest is has a separate existence, time is then just a word, a badly defined one at that. Until we (scientists included) have agreed what the word defines, we can't speculate about its nature nor make assertions about what it can or can’t do. So "what is time" is first and foremost a semantic problem. We must define the word first - what do we collectively mean by time? Below are the two notions that, together, show time is merely an intermediary word - an abstract, or a shorthand - and is hence very simple to explain:- 1. There are TWO root dictionary definitions of time:- a) as an abstract framework for measuring, reference and indexing events (i.e. the t in science); and b) as a non-specific collective term that refers to events (the unfortunate phrase 'time passing' is only actually evidenced by events happening).

These definitions are subtly but crucially different, 2. Period (or interval or duration) appears to justify the existence of time; after all period is defined as a division of time. But we can show that period and interval are definable in terms of events only. (For some people it's "persistence" that is the sticking point...it expresses the same condition as interval, and can also be de-constructed) And once you have defined period in terms of events, time itself becomes redundant. This is the tricky, slippery, but crucial piece to understand; but it wiles away time. The above two points, taken together, determine that time can always be expressed explicitly in terms of something else - events (or happenings, or change if you prefer); and hence time ceases to be a necessary fundamental - it's a useful abstract. Everything can be explained outside of the need for the word time [and so ‘puff’' - time disappears!]. Events - time merely references events. The underlying fundamental is events. Time is merely an intermediary abstract. A more complete explanation to be found here:- Original questions: 1. In physics, what is the definition of time? 2.

How would you respond to the argument that time is not real and is merely a cognitive construct that facilitates our mental perception of motion or physical change? The first question is not a simple question, but it is easy to answer (see answers of other responders). The second question is a simple question, but it is difficult to answer (I will try to answer it nevertheless). To answer this question we must first agree on what we mean by "real". Something is "real" if it has physical existence, whether or not there is a brain to perceive and/or record it. Then we have to define "fundamental" if only to avoid confusing it with "real". Something is "fundamental" if it is "real" and if it is the source (not the product) of other things or if it defines the behavior of something that is fundamental. Thus, "fundamental" is a subset of "real"; something can be "real" but not necessarily be "fundamental". Let's start by selecting the "stuff" of the universe that are definitely fundamental. Space, of course, is fundamental and - as all modern physicists know - is not empty. The elementary particles and their energy fields (fields for short) are fundamental.

Arguably, all particles and their fields (abbreviated as PF) are "condensations" or "manifestations" of space (check the wave structure of matter theory). PFs can coalesce and form larger objects. PFs/objects change their positions relative to other PFs/objects, i.e. they move. The relative motion between PFs/objects can be quantified as "speed" and, if you include the relative direction they move, then we call this "velocity". For motion to occur there should be at least two PFs/objects in space that are changing their positions relative to each other. Motion is always "relative" and it follows that speed/velocity is always relative, with one possible exception- the speed of light. But that's a different subject and we don't want to digress. Motion is "real" but is it "fundamental"? At first thought, it seems that motion is not fundamental since it requires PFs/objects, but since PFs always move relative to other PFs, then we can make a case that motion is indeed fundamental. See how I defined “fundamental” above (cheating?).

Since motion is fundamental then it has to be real-- motion occurs whether or not there is a brain to perceive and/or record it. There are perhaps a hundred other ways of defining TIME. The problem is not that these definitions are right or wrong... they can all be right! The problem is that none of these definitions tell us explicitly that time is "real" (see definition of "real" above) and none of these definitions tell us explicitly that time is "fundamental" (see definition of "fundamental" above). For example, when we define an "atom" we say that an atom is the "fundamental" unit of matter. Of course, we know that there are quarks and electrons so this definition is no longer true. At any rate, is time a fundamental unit of something like motion? No. Nobody defines time this way. Time is not synonymous with "motion", nor does it indicate "directly" that something is changing in a particular way or direction (the arrow of time). But if you are equating TIME with MOTION then this argument will not lead us to any meaningful conclusion. Let's revisit the concept of "real" and "fundamental" in relation to these three major scientific epochs: 1.

Pre-Galilean (PG), 2. Galilean-Newtonian (GN), 3. Relativity-Quantum (RQ). I was hoping to have a fourth one - 4. Neomorphysics (NM) - but not until I succeed in convincing Neo that TIME (the way it is defined in science and used in equations) is only a "concept", not a "real" entity - a colossal obstacle imposed by our brains in further understanding reality! 1. Pre-Galilean (PG): matter, force, energy, motion, time, and space are considered "real" and "fundamental". The definition of "real" is somewhat different in that something can be "real" even though it has no "physical existence". No distinction between physics and metaphysics:"real"="meta-real". The atom is the fundamental unit of matter. Concept of inertia is absent (or not well recognized). Concept of energy and force is not well developed and metaphysical. Force is emphasized in explaining motion. Space is void or empty. Time is fundamental and defined in terms of cyclical events (e.g. day-night). 2.

Galilean-Newtonian (GN): matter, force, energy, motion, time, and space are considered "real" and "fundamental". The distinction between "physical" and "metaphysical" has started but remains incomplete, so "real" can still mean existing in the physical or metaphysical sense. Evidence of something more fundamental than the atom is accumulating. The recognition of INERTIA and the modelling of energy/forces as FIELDS are the most revolutionary scientific achievements of this epoch. Inertia is emphasized in explaining uniform motion and change in motion is attributed to force. Time is considered fundamental; in fact, net force is defined as the TIME-rate of change in momentum. FORCE LAWS have been established. However, force is still conceptualized as a "metaphysical" entity (action-at-a-distance). Concept of energy transfer and force is well developed. HEAT and kinetic energy is well understood, as well as the conservation principles and the concept of ENTROPY. Although there is increasing understanding of the inter-convertibility of matter and energy, matter and energy are still considered as separate entities- not one and the same.

Space is still regarded as void or empty; however, the concept of an ETHER has dominated scientific thought during the latter part of this epoch. The ether is regarded as "something" that permeates SPACE - a universal frame of reference from which all motion can be measured and a medium for electromagnetic waves to propagate. TIME and LENGTH are considered fundamental and absolute- i.e. not influenced by inertia/motion. Some clues of subatomic particles and the quantized nature of matter and energy. 3. Relativity-Quantum (RQ): Major change in our perception of reality. We are still in this epoch which we fondly call the Age of Modern Physics. Matter=Energy: this is fundamental. Motion and time are considered real and fundamental but the relationship between the two has not been adequately explained. SPACE (not Coke) is the "real" thing. The ETHER was killed right from the get-go, so it's not really a part of this epoch (just mentioned it because of it's conceptual relevance). Killing the ether concept resulted in major paradigm shifts. TIME and LENGTH are no longer absolute quantities - they depend on the inertial state and motion of the part of space where the measurements are made. Speed of light is the new constant.

All matter and energy (fields) are QUANTIZED (and that includes your nose and brain). Space is no longer empty; it is considered "real" and "fundamental"; it is not inert either. Quantum particles (called virtual particles) can bubble out from or dissolve into space (now called "quantum foam"). FIELDS are viewed as "distortions" "warpings" of SPACE or SPACE-TIME, if you will. This is true for ALL FIELDS, including gravitational and electric fields. Matter=Field but an intuitive way to think of this is that matter is the "dense" core of space and the associated field is the wave-like extensions of the core. Thus, the particle-wave duality is now a particle-wave unity. Gravity, electric force, and other forces are NOT REALLY FORCES- they don't push or pull. You can call them pseudo-forces or say no such thing as force anymore. Motion is still attributed to INERTIA but no modern definition of inertia yet. What's intuitively more appealing is the concept of "GEODESICS" (space-warping): objects (e.g.

planets/moons) simply follow the space (spacetime if you will) geodesic or "curvature" as they appear to "orbit" around their mommas. TIME remains enigmatic. It must be a result of some motion or something in space changing. What motion or change? I dunno. For someone to say, event A happened before B, event A must first be perceived and "stored" in memory (change in brain physiology first, but change in wiring or circuitry if long enough) before event B. Otherwise, one can't tell which event is past, present, and future. Relativity also demolished the concept of simultaneity. Without simultaneity can we have TIME? Sure we can, but which of these three observations is correct - event A then B, event B then A, or event A and B simultaneously? The answer depends on your frame of reference. What's worse, all equations in physics are "time-neutral" or "symmetric" in regards to time, i.e. none of the fundamental equations of relativity or quantum mechanics will reveal if a process is going forward into the future or going backwards into the past.

The basic "Equations of Nature" tell us that one variable is related in some quantitative way with another variable. NONE of the equations tell us that one variable is the "cause" and the other is the "effect". We definitely need some guidance from our memory circuitry. In this sense, TIME (the way it is conceived by humans) is NOT REAL. In strict logic terms, SPACE does not require a definition since it is a physics "fundamental". In math, we call this an AXIOM. That said, we can still define SPACE independent of coordinates (e.g. x, y, z). For example, I can say that SPACE is the fundamental substance of the physical universe from which all (or most) matter, energy, fields, and motion arise. You can't do the same with TIME because time is NOT fundamental. With this definition of SPACE, we can construct (mentally) our coordinate system. The only intuitive coordinate system, as far as the human brain is concerned, is the 3D Cartesian coordinate system. Adding a 4th, 5th, 11th, or nth dimension is moving out of the realm of intuition.

What I'm trying to point out is that SPACE is the fundamental physical entity and the COORDINATE SYSTEM is a mental construct or model that helps us understand SPACE and everything else derived from space (matter/fields/virtuals) and their behavior (motion). TIME is definitely a mental construct since you have to define it first based on MOTION and an imaginary coordinate (line with an arrowhead) and from there work your way back to SPACE. To paraphrase: Nothing is nothing! Space and motion is everything! Space is differentiated into the "fundamental" stuff: foam, fields, form, and their "dark" counterparts. Motion is the behavior of space and all of it's derivatives. Fundamental stuff "interact" and give rise to motion and higher-order stuff. Time is not real, nor is it fundamental (so don't say "fime"). Time is our brain's way of tracking the motion of some (not all) derivatives of space. Without motion and brain, there is no time! Without time and brain, there is still motion, space, and all it's derivatives, except brain (which is a very high-order derivative of space). ------ Added 5/5/2015 (from one of my comments).

Change is fundamental behavior of space--it always means a change in the elements of space (space = fields and field quanta). Time is how a complex recording device (e.g. brain) perceives/interprets the changing elements or behavior of space. Because time can be derived from (and defined on the basis) of some "change in space" -- including the tendency of fields/quanta to change towards a state of low energy (entropy) -- time is not fundamental. Fields and quanta are-- and so is Space! 5.1k Views · View Upvotes · Answer requested by Quora User Matthew Marsden , A Brief History of Timelessness Updated Feb 9, 2015 Hi Quora, re “What IS (the definition) of Time?” – this question, variations of it, appear on a number of QUORA pages, I can’t link to my initial answer, so I hope you don’t mind if post it here also... (saves a lot of typing ) - also I have posted a related question on QUORA, see below.

Having researched, and written a lot on "the theory of time" ( see links at end), I think we will find there is a critical step that is almost universally ignored wherever we are faced with the question “What IS time?”, (i.e so that it can be "defined" ), and ignoring this step may lead to the endless, growing diverse, incompatible, unchecked, and unconfirmable , speculation that follows the question. (the first step being to actually check the question is valid). With respect, If you look at the 93+ “answers” on this page, and the thousands of answers to similar “What IS Time” forums etc on the net (as I am familiar with), you will find a number of overlooked, or ignored, logical, practical, and scientific problems, extraordinary to all of general knowledge and “science”. E.g. 1-There are an extraordinarily wide range of fundamentally conflicting opinions, (often stated as fact), about this “time” thing. 2-No scientist’s seem to consider that where a theory produces endless conflicting possibilities this is a strong indicator that the theory may be entirely wrong, or have a critical flaw in it’s conception.

3-despite a plethora of opinion (lay and scienticfic), virtually all, if not all, posters do not defines specific hypothesises re specific areas of their version of the theory of time, and describe scientific experiments, as per the scientific method , to test those hypothesis. (in other word’s, for some obscure reason, “the theory of time” seems to be given the status of accepted, even though there is no single clear accepted definition of the theory, let alone definitions of scientific experiments, as per the scientific method , to prove aspects of the theory). 4-re the question, “What IS time?”, few people seem to even check that the question itself is valid... but instead assume it is, and thus assume that the poser of the question “What IS time?”, is certain there IS a thing called “time”, i.e. they have reasonable proof.... but just wants to know what “it” “IS”. Re point 4, the question, “What IS time?”, the first response should logically be to ask the poser of the question for their precise definition, theory, and reasonable proof/experiment, showing that the “thing” they are asking about probably “exists”...

( so we can say what it “is”). Consider the question “what IS the MAGIC of Harry Potter?” This question taken literally is invalid. (Sensibly) there IS no MAGIC of Harry Potter, only the fictitious idea of magic. Anyone investigating the question meticulously... (rather than just assuming MAGIC exists, and so the only question is what IS magic), should check the books and films, and their sources, and should find only ideas and special effects,,, ie no magic to be explained. So re the question, “What IS time?”, I would suggest, rather than everyone just ASSUMING there IS a thing called “time”, and rushing off like a crowed of villagers hunting a ghost, we stop, clear our minds of all assumptions, and ask... Q-What do we actually seem to observe? To which I would suggest... A- We actually, and only, seem to observe... 1 - That Matter(energy) seems to exist, and 2 - That matter seems to be able to be moving, changing and interacting in all possible directions. From there... rather than jumping to the conclusion that some variation of the various theories of time, must be correct... e.g.

-----------the theory of time------------, - there is, an invisible intangible place or thing called ‘the future’ , ‘out of’ which things and events come, and, - there is, an invisible intangible place or thing called ‘the past , ‘into’ which things and events ‘go’, and, - there is, an invisible intangible thing called ‘Time’ , that, extra to energy, is needed for things to move, and “passes” in an undefined way between the invisible Future, and invisible past... (etc) ------------------ Instead of just blindly accepting the above, and based on the fact that we seem to actually, and only, seem to observe... 1-That Matter(energy) seems to exist, and 2-That matter seems to be able to be moving, changing and interacting in all possible directions. And that despite constant talk, we do not actually observe, -a past, -anything going into a past, or, -anything coming out of a future I suggest, instead of asking “what is (the definiton of) time?” We ask the hopefully more scientific, and less leading question... “IF matter/energy, JUST(as in only), exists, moves changes, and interacts...

would this be enough to mislead us into thinking there may be a thing called ‘Time’ ? ” I think if people focus on this question, it may produce more logical, tangible, and actually scientifically testable results. (in other words, while scientists may accept 'definitions' like "time IS that which clocks measure" - perhaps a "clock" is just a misleadingly named motor - and as such only "measures" the flow of energy from a spring etc through a mechanism - an in no way proves or measures the existience of a past, a future or thing called time) Updated Aug 2, 2014 The universe we exist in has been changing since the Big Bang and has since been expanding at an accelerating rate, though the rate of acceleration is itself apparently decreasing. The point is, our space is dynamic and, hence, particle-fields are continuously moving/interacting/changing. This change occurs, whether we perceive it or not, in the 3 dimensions of inflationary space and the 4th dimension of time. Time is inherent in a dynamic universe (whether expanding, contracting or ripping) and inseparable from the fabric of its space.

Great minds have tried and failed to formulate a universally-accepted definition of time, mostly because the reasoning inevitably becomes circular. Time -> Change -> Time. Is Time causal, is it simply permissive of physical change, or is it actually birthed by change (such as the Big Bang) or just a mere expression of change? Does the difference matter? The principle of Invariant Light Speed, regardless of frame of reference, dictates that the only solution for a photon to reach the moving FOR is by Time Dilation. If Time can thus be manipulated by physical factors, then time is real. Elon Musk can manipulate time if he builds a pulsed fusion engine that propels a rocket to 0.9 c, thereby slowing the passage of time for its passengers. Time is fundamental in the sense that it is part of the framework of our universe. Our universe would be vastly different if it did not have the 4th Dimension of Time, analogous to the difference between a 2-Dimensional painting and a 3-Dimensional sculpture. The universe, as well as any meaningful manifestation of Time, began with the Big Bang. If the universe ends in the Big Crunch, then Time, as we know it, ends as well. Time is asymmetric.

We do not know why the balance of phenomena after the Big Bang led to Time going forward instead of backward, just as we do not know why matter, and not anti-matter, predominates. What is obvious is that space would not have inflated if Time went backwards. Perhaps it is the inflating characteristic of the universe that gave rise to Time. Perhaps Time goes backwards when the universe contracts (Anti-Time?). I actually do not think that Time is necessarily linear, although we perceive it as an Arrow. It might be branching, looping, or going backwards all the "time", and we just can't perceive it doing so, just like characters in a computer game won't know either. Speed and Velocity 1-D Kinematics - Lesson 1 - Describing Motion with Words Speed and Velocity Acceleration Just as distance and displacement have distinctly different meanings (despite their similarities), so do speed and velocity. Speed is a scalar quantity that refers to "how fast an object is moving." Speed can be thought of as the rate at which an object covers distance. A fast-moving object has a high speed and covers a relatively large distance in a short amount of time.

Contrast this to a slow-moving object that has a low speed; it covers a relatively small amount of distance in the same amount of time. An object with no movement at all has a zero speed. Velocity as a Vector Quantity Velocity is a vector quantity that refers to "the rate at which an object changes its position." Imagine a person moving rapidly - one step forward and one step back - always returning to the original starting position. While this might result in a frenzy of activity, it would result in a zero velocity. Because the person always returns to the original position, the motion would never result in a change in position. Since velocity is defined as the rate at which the position changes, this motion results in zero velocity. If a person in motion wishes to maximize their velocity, then that person must make every effort to maximize the amount that they are displaced from their original position. Every step must go into moving that person further from where he or she started. For certain, the person should never change directions and begin to return to the starting position. Velocity is a vector quantity. As such, velocity is direction aware. When evaluating the velocity of an object, one must keep track of direction.

It would not be enough to say that an object has a velocity of 55 mi/hr. One must include direction information in order to fully describe the velocity of the object. For instance, you must describe an object's velocity as being 55 mi/hr, east. This is one of the essential differences between speed and velocity. Speed is a scalar quantity and does not keep track of direction; velocity is a vector quantity and is direction aware. Determining the Direction of the Velocity Vector The task of describing the direction of the velocity vector is easy. The direction of the velocity vector is simply the same as the direction that an object is moving. It would not matter whether the object is speeding up or slowing down. If an object is moving rightwards, then its velocity is described as being rightwards. If an object is moving downwards, then its velocity is described as being downwards. So an airplane moving towards the west with a speed of 300 mi/hr has a velocity of 300 mi/hr, west. Note that speed has no direction (it is a scalar) and the velocity at any instant is simply the speed value with a direction. Calculating Average Speed and Average Velocity As an object moves, it often undergoes changes in speed.

For example, during an average trip to school, there are many changes in speed. Rather than the speed-o-meter maintaining a steady reading, the needle constantly moves up and down to reflect the stopping and starting and the accelerating and decelerating. One instant, the car may be moving at 50 mi/hr and another instant, it might be stopped (i.e., 0 mi/hr). Yet during the trip to school the person might average 32 mi/hr. The average speed during an entire motion can be thought of as the average of all speedometer readings. If the speedometer readings could be collected at 1-second intervals (or 0.1-second intervals or ... ) and then averaged together, the average speed could be determined. Now that would be a lot of work. And fortunately, there is a shortcut. Read on. The average speed during the course of a motion is often computed using the following formula: In contrast, the average velocity is often computed using this formula Let's begin implementing our understanding of these formulas with the following problem: Q: While on vacation, Lisa Carr traveled a total distance of 440 miles. Her trip took 8 hours. What was her average speed?

To compute her average speed, we simply divide the distance of travel by the time of travel. That was easy! Lisa Carr averaged a speed of 55 miles per hour. She may not have been traveling at a constant speed of 55 mi/hr. She undoubtedly, was stopped at some instant in time (perhaps for a bathroom break or for lunch) and she probably was going 65 mi/hr at other instants in time. Yet, she averaged a speed of 55 miles per hour. The above formula represents a shortcut method of determining the average speed of an object. Average Speed versus Instantaneous Speed Since a moving object often changes its speed during its motion, it is common to distinguish between the average speed and the instantaneous speed. The distinction is as follows. Instantaneous Speed - the speed at any given instant in time. Average Speed - the average of all instantaneous speeds; found simply by a distance/time ratio. You might think of the instantaneous speed as the speed that the speedometer reads at any given instant in time and the average speed as the average of all the speedometer readings during the course of the trip.

Since the task of averaging speedometer readings would be quite complicated (and maybe even dangerous), the average speed is more commonly calculated as the distance/time ratio. Moving objects don't always travel with erratic and changing speeds. Occasionally, an object will move at a steady rate with a constant speed. That is, the object will cover the same distance every regular interval of time. For instance, a cross-country runner might be running with a constant speed of 6 m/s in a straight line for several minutes. If her speed is constant, then the distance traveled every second is the same. The runner would cover a distance of 6 meters every second. If we could measure her position (distance from an arbitrary starting point) each second, then we would note that the position would be changing by 6 meters each second. This would be in stark contrast to an object that is changing its speed. An object with a changing speed would be moving a different distance each second. The data tables below depict objects with constant and changing speed. Now let's consider the motion of that physics teacher again. The physics teacher walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North. The entire motion lasted for 24 seconds.

Determine the average speed and the average velocity. The physics teacher walked a distance of 12 meters in 24 seconds; thus, her average speed was 0.50 m/s. However, since her displacement is 0 meters, her average velocity is 0 m/s. Remember that the displacement refers to the change in position and the velocity is based upon this position change. In this case of the teacher's motion, there is a position change of 0 meters and thus an average velocity of 0 m/s. Here is another example similar to what was seen before in the discussion of distance and displacement . The diagram below shows the position of a cross-country skier at various times. At each of the indicated times, the skier turns around and reverses the direction of travel. In other words, the skier moves from A to B to C to D. Use the diagram to determine the average speed and the average velocity of the skier during these three minutes. When finished, click the button to view the answer. Acceleration - Physics Video by Brightstorm Acceleration M.Ed., George Washington University Dept. chair at a high school Matt is currently the department chair at a high school in San Francisco.

In his spare time, Matt enjoys spending time outdoors with his wife and two kids. Thank you for watching the video. To unlock all 5,300 videos, start your free trial. M.Ed., George Washington University Dept. chair at a high school Matt is currently the department chair at a high school in San Francisco. In his spare time, Matt enjoys spending time outdoors with his wife and two kids. Share acceleration rate of change velocity Okay let's talk about acceleration. You've all heard about acceleration when you watch a car advertisement, this car goes 0 to 60 in 5.2 seconds. What they're really telling you how well that car accelerates. So acceleration is the rate of change of velocity, how quickly it can get from a low speed 0 to a very high speed okay? So let's first look at the units because the units for acceleration can often times be confusing okay? So we have the rate of change of velocity so we have a final velocity minus an initial velocity over time okay?

Now remember velocity is like like meters per second it's a distance over time, so if you have a distance over time minus the distance over time we end up with distance over time divided by time, so what we're going to do is we're going to move both of our time units down to the denominator and we're going to have a distance over time squared okay? So let's look at an example of how we could solve an acceleration problem okay? Like that car that was accelerating, how fast was that rate of acceleration okay? So let's say that car goes from 0 kilometers per hour to 100 kilometers per hour in 10 seconds okay? I need to take my final velocity 100 kilometers an hour minus my initial velocity 0 kilometers an hour, remember to include your units, sometimes you can get confused if you drop your units and you don't know what you're talking about okay? So we've got that over 10 seconds okay? Now notice I have seconds here and hours here, is that a problem? No it's not, we can actually use units where we have hours, second hours or hours seconds those are fine okay?

So when we solve that 100-0 is a 100 divided by ten equals 10 kilometers per hour second okay? So that is our rate of acceleration 10 kilometers per hour second. One final note about acceleration, remember we're talking about changes in velocity and velocity involves not only a distance over time but in direction so we have going the same speed but we're changing direction our velocity is changing and our acceleration will be accelerating as we go around the curve so it's not just accelerating going straight we can also as we turn keeping the same velocity we can also accelerate even our speed remains the same and that's important to remember that acceleration.

Question: In physics, what is defined as the rate of change of velocity with time?
Answer: ACCELERATION